By Gheorghe D. Mateescu, Adrian Valeriu
Not like so much really expert books in this topic that emphasize the mathematical foundations of 2nd NMR, this booklet deals an experimentally-based, transparent rationalization of the density-matrix and product operator remedies therefore permitting non-experts to determine sequences of various levels of complexity.
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Extra info for 2D Nmr: Density Matrix and Product Operator Treatment
74) ⎥ 1 ⎥⎦ Two important changes have been induced by the 180o pulse. First, all single quantum coherences were conjugated and changed sign. 38 Density Matrix Treatment This means that all x-components changed sign while the y-components remained unchanged: M T = M x + iM y − M T* = − M x + iM y This shows, indeed, that all four vectors rotated 180o around the yaxis. Second, coherences corresponding to fast precessing nuclei were transferred in "slots" corresponding to slow evolution. This means the vectors also changed labels.
Those in states 2 and 4 are slow. Likewise, carbons in states 1 and 2 are fast, those in states 3 and 4 are slow. 54), at t(0) half of MzH is due to fast protons (d11 - d33) and the other half to slow protons. 6 with 13 and 24, respectively. For carbon, it is 12 and 34. Speaking of C-H pairs, a proton can add or subtract to the field "seen" by the carbon. Therefore the carbon will be fast if it pairs with a spin-up proton or slow if it pairs with a spin-down proton. The carbon spins will have a similar effect on protons.
87) respectively. 9. 89) M ' = − M o' a * / 2 = (−iM o' / 2) exp(−iΦ ) These are the two peaks of the uncoupled nuclei. 88). The culminating point of INADEQUATE is the selective detection of MT(cpl). 89)]. They can be discriminated by cycling F and properly choosing the receiver phase Y [the detected signal S = MT exp(-iY)]. The table below shows that two cycles are sufficient to eliminate MT(ncpl). Cycle F Y 1 2 (1+2) 0 90o 0 -90o ncpl -------------expi(F-Y) 1 -1 0 cpl -------------expi(-F-Y) 1 1 2 Even small imperfections of the rf pulse will allow leakage of the strong undesired signal into the resultant spectrum.
2D Nmr: Density Matrix and Product Operator Treatment by Gheorghe D. Mateescu, Adrian Valeriu